1. Derivative Part 2

2. Definition The derivative of a function f is another function f ’ (read “f prime”) whose value at any number x is : Provided that this limit exists and is not  or -   If this limit does exist  f differentiable at c  Other way  if f differentiable at x1 then f ‘(x1) exist  If a function differentiable at every riil number in their domain then f called differentiable function

3. Soo if x1 belong to domain then

4. Add Note : If we take then

5. Differentiability Implies Continiuty Ex. Check if continue at x=0 and differentiable at x=0?

6. The Constant Rule

7. The Power Rule

8. The Constant Multiple Rule

9. The Sum and Difference Rules

10. Derivatives of Sine and Cosine Functions

11. The Product Rule

12. The Quotient Rule

13. Derivatives of Trigonometric Function

14. Leibniz Notation for Derivatives Ultimately, this notation is a better and more effective notation for working with derivatives.

15. Teorema If and differentiable function then

19. The Chain Rule

20. The General Power Rule

21. Summary of Differentiation Rules

22. Exercise 1 Suppose f with Find a and b such as f continue at x=0 but f’(0) does’nt exist

23. Exercise 2 Check if the function differentiable at 0 ??

24. Ex3 Check if the function Differentiable at x=0

25. Ex 4 Find the derivative from the function :

26. Ex 5 Calculate d/dx(  x  ) then show the function y=  x  satisfied yy’=x, x  0

27. Ex 6 Find the derivative from the invers function